The assignee of the present invention designs and manufactures spacecraft for operation in, for example, geosynchronous and low earth orbits. In an on-orbit configuration, such spacecraft may have one or more deployed appendages, such as solar arrays or payload components. Such an appendage may be attached to a main body of the spacecraft by way of a mechanical coupling. In view of a requirement to minimize hardware mass, a highly rigid mechanical coupling may be impractical. As a result, dynamic response (cyclic relative motion between the appendage and the main body) of the deployed system that may result from disturbances such as a thruster firing must be anticipated. It is desirable to limit the amplitude of the dynamic response, without increasing hardware mass.
One technique to reduce dynamic response to the deployed system resulting from a thruster firing for an orbit maneuver is disclosed in “Flycast Maneuver for Shuttle Radar Topography Mission”, Thomas A. Trautt, published in 35th Aerospace mechanism symposium, 2001, pg. 95-107 (hereinafter, “Trautt”). Trautt discloses pulsing a thruster prior to and after an orbit maneuver according to a sequence illustrated in FIG. 1. The thruster pulse duration is set at T/6, where T is the calculated natural period of a system that includes a deployed boom. Following the pulse, and prior to the orbit maneuver, a first coast interval, also having a duration of T/6 is executed, a coast interval being a period of time in which the thruster is not fired. At the end of the orbit maneuver a second coast interval of duration of T/6 is executed, followed by a second thruster pulse also having a duration of T/6. Trautt refers to the above described sequence, which will be referred to herein as a “single pulsed single coast”, or “SPSC” sequence, as a “Flycast Maneuver”.
Where the period T is accurately calculable, the techniques disclosed in Trautt are effective to reduce the maximum deflection, and substantially eliminate oscillation of the appendage, as may be observed in FIG. 2. Detail A of FIG. 2 illustrates the analytically determined appendage deflection ‘q’ versus time during and after an orbit maneuver in the absence of the SPSC sequence. In the illustrated example, an average deflection amplitude of qSS occurs during the orbit maneuver and an average deflection amplitude of 2 qSS occurs subsequent to the orbit maneuver. Detail B illustrates the analytically determined appendage deflection ‘q’ versus time for an orbit maneuver accompanied by a pre-and post-maneuver SPSC sequence is executed, assuming perfect knowledge of T. With the assumption that T is perfectly calculable, the SPSC sequence is seen to be effective to reduce the maximum deflection by about 50% and to substantially eliminate post-maneuver oscillations.
In many actual space systems, however, there is significant unavoidable uncertainty in the value of T. For example, referring now to Detail C of FIG. 2, where an actual value of T is 20% different than calculated, a substantially higher amount of deflection and continued post-maneuver oscillation of the appendage can result.
As a result, an improved pre-and post-maneuver thruster firing strategy is desirable.